Automatic detection of malignant lung nodule can potentially play an important role for lung cancer detection. A crucial component of this detection process is accurate lung nodule segmentation. Due to the small size of the nodule, variance in density values and presence of peripheral blood vessels, common image segmentation methods fail to perform satisfactorily. We are developing an image segmentation using computational optimization techniques. The optimization problem is formulated to achieve noise reduction, edge crispening and production of homogeneous and uniform regions. This is followed by edge detection, contour completion and combination to form the final segmentation. Our preliminary results suggest that the method is able to produce segmentation with a faily accurate edge description of the nodule. We intend to further test and strengthen our method.